Physical Meaning of Hermiticity and Shortcomings of the Composite (Hermitian + non-Hermitian) Quantum Theory of Gunther and Samsonov

TL;DR

This paper clarifies the physical meaning of Hermiticity and critically examines a proposed generalized quantum theory combining Hermitian and non-Hermitian operators, highlighting its inconsistencies and limitations.

Contribution

It provides a simple physical interpretation of Hermiticity and analyzes the shortcomings of Gunther and Samsonov's composite quantum theory.

Findings

The composite theory has a dynamical inconsistency.

It cannot adequately replace standard measurement theory.

Hermiticity has a clear physical meaning, unlike the generalized approach.

Abstract

In arXiv:0709.0483 Gunther and Samsonov outline a ``generalization'' of quantum mechanics that involves simultaneous consideration of Hermitian and non-Hermitian operators and promises to be ``capable to produce effects beyond those of standard Hermitian quantum mechanics.'' We give a simple physical interpretation of Hermiticity and discuss in detail the shortcomings of the above-mentioned composite quantum theory. In particular, we show that the corresponding ``generalization of measurement theory'' suffers from a dynamical inconsistency and that it is by no means adequate to replace the standard measurement theory.